A LED light source can be constructed from a LED module placed in a fixture having a lens. The lens can serve to direct light from the LED module to an environment in which the LED light source is placed. A LED module typically distributes light in a Lambertian radiation pattern. In other words, the majority of the light emitted by the LED module is within a half angle of 60 degrees from the vertical axis of an emitting face of the LED module. This illumination pattern, however, may not be desirable for ceiling light fixtures, or other fixtures for which it is desirable that light is distributed using a wide angle pattern. In particular, this light pattern may not be desirable for LED modules provided on a top surface of a hanging fixture, where the LED modules illuminate a ceiling. Instead, it may be desirable for light emitted by the LED modules to be shifted such that the emitted light falls in a region substantially near a plane of the emitting face of the LED module (e.g., in a wide angle).